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%I #4 Feb 07 2014 05:09:02
%S 81,344,344,1472,2064,1472,6368,12408,12408,6368,27280,76188,104248,
%T 76188,27280,115584,455160,912912,912912,455160,115584,494592,2721900,
%U 7660840,11767448,7660840,2721900,494592,2139648,16378560,64312576
%N T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the minimum minus the upper median minus the lower median of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one
%C Table starts
%C .......81........344.........1472...........6368............27280
%C ......344.......2064........12408..........76188...........455160
%C .....1472......12408.......104248.........912912..........7660840
%C .....6368......76188.......912912.......11767448........141627680
%C ....27280.....455160......7660840......141627680.......2375768088
%C ...115584....2721900.....64312576.....1709556016......39693722016
%C ...494592...16378560....541081120....20834106592.....680588692128
%C ..2139648..100568160...4737777088...274803913264...12934636122240
%C ..9166080..600811200..39760171616..3352960252480..219580118935904
%C .38836224.3592908000.333806884096.40937682523424.3692772114256256
%H R. H. Hardin, <a href="/A237384/b237384.txt">Table of n, a(n) for n = 1..144</a>
%F Empirical for column k:
%F k=1: a(n) = 336*a(n-4) for n>5
%F k=2: a(n) = 1320*a(n-4) for n>6
%F k=3: a(n) = 10380*a(n-4) -26935616*a(n-8) for n>11
%F k=4: [order 16] for n>20
%F k=5: [order 36] for n>41
%e Some solutions for n=3 k=4
%e ..0..1..0..0..0....0..1..0..1..0....0..1..0..0..2....0..0..0..1..2
%e ..1..2..2..2..1....1..1..0..0..1....0..1..1..1..2....0..2..1..0..0
%e ..0..2..0..1..2....0..0..0..0..0....2..0..0..1..2....1..0..1..1..1
%e ..2..2..1..0..0....1..0..0..1..1....2..0..1..0..0....0..1..1..1..2
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 07 2014
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